The divergence of F is
div(F ) = ∂(x + yz)/∂x + ∂(y + xz)/∂y + ∂(z + xy)/∂z
div(F ) = 1 + 1 + 1
div(F ) = 3
The divergence of the vector field is equal to 3
Data;
(x+yz)i(y + xz)j(z+xy)kDivergence of Vector FieldTo find the divergence of the vector field, we have to differentiate the i, j and k component of the vector.
[tex]div F = \frac{\delta}{\delta x} (x+yz) + \frac{\delta}{\delta y} (y + xz) + \frac{\delta}{\delta z} (z + xy)\\div F = (1+0)+(1+0)+(1+0)\\div F = 1 + 1 + 1 \\div F = 3[/tex]
The divergence of the vector field is equal to 3
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Instructions: Determine whether the following polygons are
similar. If yes, type in the similarity statement and scale factor. If
no, type 'None' in the blanks.
Answer:
None
Step-by-step explanation:
The given angles aren't equal which is needed for the polygon to be similar
No, the following polygons are not similar.
Used the concept of a similar figure that states,
In terms of Maths, when two figures have the same shape but their sizes are different, then such figures are called similar figures.
Given that,
Two polygons EFGH and JKLM are shown in the image.
Now the corresponding sides of both figures are,
EF = 27
JK = 63
And, EH = 27
JM = 63
Hence, the ratio of corresponding sides is,
EF/JK = 27/63
= 9/21
= 3/7
EH/JM = 27/63
= 3/7
So their corresponding sides are equal in ratio.
But their corresponding angles are not the same.
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[infinity]
Substitute y(x)= Σ 2 anx^n and the Maclaurin series for 6 sin3x into y' - 2xy = 6 sin 3x and equate the coefficients of like powers of x on both sides of the equation to n= 0. Find the first four nonzero terms in a power series expansion about x = 0 of a general
n=0
solution to the differential equation.
У(Ñ)= ___________
Recall that
[tex]\sin(x)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex]
Differentiating the power series series for y(x) gives the series for y'(x) :
[tex]y(x)=\displaystyle\sum_{n=0}^\infty a_nx^n \implies y'(x)=\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]
Now, replace everything in the DE with the corresponding power series:
[tex]y'-2xy = 6\sin(3x) \implies[/tex]
[tex]\displaystyle\sum_{n=0}^\infty (n+1)a_{n+1}x^n - 2\sum_{n=0}^\infty a_nx^{n+1} = 6\sum_{n=0}^\infty(-1)^n\frac{(3x)^{2n+1}}{(2n+1)!}[/tex]
The series on the right side has no even-degree terms, so if we split up the even- and odd-indexed terms on the left side, the even-indexed [tex](n=2k)[/tex] series should vanish and only the odd-indexed [tex](n=2k+1)[/tex] terms would remain.
Split up both series on the left into even- and odd-indexed series:
[tex]y'(x) = \displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} + \sum_{k=0}^\infty (2k+2)a_{2k+2}x^{2k+1}[/tex]
[tex]-2xy(x) = \displaystyle -2\left(\sum_{k=0}^\infty a_{2k}x^{2k+1} + \sum_{k=0}^\infty a_{2k+1}x^{2k+2}\right)[/tex]
Next, we want to condense the even and odd series:
• Even:
[tex]\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2k+2}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2(k-1)+1}x^{2k}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2k-1}x^{2k}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty \bigg((2k+1)a_{2k+1} - 2a_{2k-1}\bigg)x^{2k}[/tex]
• Odd:
[tex]\displaystyle \sum_{k=0}^\infty 2(k+1)a_{2(k+1)}x^{2k+1} - 2\sum_{k=0}^\infty a_{2k}x^{2k+1}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2(k+1)}-2a_{2k}\bigg)x^{2k+1}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1}[/tex]
Notice that the right side of the DE is odd, so there is no 0-degree term, i.e. no constant term, so it follows that [tex]a_1=0[/tex].
The even series vanishes, so that
[tex](2k+1)a_{2k+1} - 2a_{2k-1} = 0[/tex]
for all integers k ≥ 1. But since [tex]a_1=0[/tex], we find
[tex]k=1 \implies 3a_3 - 2a_1 = 0 \implies a_3 = 0[/tex]
[tex]k=2 \implies 5a_5 - 2a_3 = 0 \implies a_5 = 0[/tex]
and so on, which means the odd-indexed coefficients all vanish, [tex]a_{2k+1}=0[/tex].
This leaves us with the odd series,
[tex]\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1} = 6\sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!}[/tex]
[tex]\implies 2(k+1)a_{2k+2} - 2a_{2k} = \dfrac{6(-1)^k}{(2k+1)!}[/tex]
We have
[tex]k=0 \implies 2a_2 - 2a_0 = 6[/tex]
[tex]k=1 \implies 4a_4-2a_2 = -1[/tex]
[tex]k=2 \implies 6a_6-2a_4 = \dfrac1{20}[/tex]
[tex]k=3 \implies 8a_8-2a_6 = -\dfrac1{840}[/tex]
So long as you're given an initial condition [tex]y(0)\neq0[/tex] (which corresponds to [tex]a_0[/tex]), you will have a non-zero series solution. Let [tex]a=a_0[/tex] with [tex]a_0\neq0[/tex]. Then
[tex]2a_2-2a_0=6 \implies a_2 = a+3[/tex]
[tex]4a_4-2a_2=-1 \implies a_4 = \dfrac{2a+5}4[/tex]
[tex]6a_6-2a_4=\dfrac1{20} \implies a_6 = \dfrac{20a+51}{120}[/tex]
and so the first four terms of series solution to the DE would be
[tex]\boxed{a + (a+3)x^2 + \dfrac{2a+5}4x^4 + \dfrac{20a+51}{120}x^6}[/tex]
Which graph is a function?
Answer:
B
Step-by-step explanation:
A function is a relation in which each input, x, has only one output, y.
There are two ways to determine if a relation is a function:
1. If each x-input has only one, unique y-output, then it's a function. If some x-inputs share the same y-outputs, it's not a function.
2. Vertical Line Test on Graphs:
To determine whether y is a function of x, when given a graph of relation, use the following criterion: if every vertical line you can draw goes though only 1 point, the relation can be a function. If you can draw a vertical line that goes though more than 1 point, the relation cannot be a function.
Since we're given a graph relation, let's test both of the answers out.
If I were to draw a vertical line in a specific place on the first graph, I'd be hitting more than one point in the coordinate plane.
If I were to draw a vertical line in a specific place on the second graph, I'd only be hitting one point in the coordinate plane.
Therefore, choice B is a function.
give ABCD is a trapizod , Ab = 13, CD= 14, BC = 15, and AD = 20 what is the area
Step-by-step explanation:
A=140sq. units
Step-by-step explanation:
ABCD
A=13
B=15
C=14
D=20
C=14×14
=196sqr.units
To calculate the volume of a chemical produced in a day a chemical manufacturing company uses the following formula below:
[tex]V(x)=[C_1(x)+C_2(x)](H(x))[/tex]
where represents the number of units produced. This means two chemicals are added together to make a new chemical and the resulting chemical is multiplied by the expression for the holding container with respect to the number of units produced. The equations for the two chemicals added together with respect to the number of unit produced are given below:
[tex]C_1(x)=\frac{x}{x+1} , C_2(x)=\frac{2}{x-3}[/tex]
The equation for the holding container with respect to the number of unit produced is given below:
[tex]H(x)=\frac{x^3-9x}{x}[/tex]
a. What rational expression do you get when you combine the two chemicals?
b. What is the simplified equation of ?
c. What would the volume be if 50, 100, or 1000 units are produced in a day?
d. The company needs a volume of 3000 How many units would need to be produced in a day?
Answer:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]V(50) = 2548.17[/tex] [tex]V(100) = 10098.10[/tex] [tex]V(1000) = 999201.78[/tex]
[tex]x = 54.78[/tex]
Step-by-step explanation:
Given
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
[tex]C_1(x) = \frac{x}{x+1}[/tex]
[tex]C_1(x) = \frac{2}{x-3}[/tex]
[tex]H(x) = \frac{x^3 - 9x}{x}[/tex]
Solving (a): Expression for V(x)
We have:
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
Substitute known values
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solving (b): Simplify V(x)
We have:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solve the expression in bracket
[tex]V(x) = [\frac{x*(x-3) + 2*(x+1)}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-3x + 2x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
Factor out x
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x(x^2 - 9)}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x^2 - 9)[/tex]
Express as difference of two squares
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x- 3)(x + 3)[/tex]
Cancel out x - 3
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)}] *(x + 3)[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Solving (c): V(50), V(100), V(1000)
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Substitute 50 for x
[tex]V(50) = [\frac{(50^2-50+2)(50 + 3)}{(50 + 1)}][/tex]
[tex]V(50) = \frac{(2452)(53)}{(51)}][/tex]
[tex]V(50) = 2548.17[/tex]
Substitute 100 for x
[tex]V(100) = [\frac{(100^2-100+2)(100 + 3)}{(100 + 1)}][/tex]
[tex]V(100) = \frac{9902)(103)}{(101)}[/tex]
[tex]V(100) = 10098.10[/tex]
Substitute 1000 for x
[tex]V(1000) = [\frac{(1000^2-1000+2)(1000 + 3)}{(1000 + 1)}][/tex]
[tex]V(1000) = [\frac{(999002)(10003)}{(10001)}][/tex]
[tex]V(1000) = 999201.78[/tex]
Solving (d): V(x) = 3000, find x
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]3000 = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Cross multiply
[tex]3000(x + 1) = (x^2-x+2)(x + 3)[/tex]
Equate to 0
[tex](x^2-x+2)(x + 3)-3000(x + 1)=0[/tex]
Open brackets
[tex]x^3 - x^2 + 2x + 3x^2 - 3x + 6 - 3000x - 3000 = 0[/tex]
Collect like terms
[tex]x^3 + 3x^2- x^2 + 2x - 3x - 3000x + 6 - 3000 = 0[/tex]
[tex]x^3 + x^2 -3001x -2994 = 0[/tex]
Solve using graphs (see attachment)
[tex]x = -54.783[/tex] or
[tex]x = -0.998[/tex] or
[tex]x = 54.78[/tex]
x can't be negative. So:
[tex]x = 54.78[/tex]
What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth.
-5.8 ft
-6.3 ft
-27.5 ft
-69.1 ft
9514 1404 393
Answer:
69.1 ft
Step-by-step explanation:
The diameter of the circle is 24 ft. The length of the arc is more than twice the diameter, so cannot be less than about 50 ft. The only reasonable choice is ...
69.1 ft
__
The circumference of the circle is ...
C = 2πr = 2(3.14)(12 ft) = 75.36 ft
The arc length of interest is 330° of the 360° circle, so is 330/360 = 11/12 times the circumference.
s = (11/12)(75.36 ft) = 69.08 ft ≈ 69.1 ft
Answer:D
Step-by-step explanation:
Find the measure of each angle in the problem. TO contains point H.
Answer:
The angles are 45 and 135
Step-by-step explanation:
The two angles form a straight line, which is 180 degrees
c+ 3c = 180
4c = 180
Divide by 4
4c/4 =180/4
c = 45
3c = 3(45) = 135
The angles are 45 and 135
Answer:
45 and 135 ...
The three sides of a triangle are n, 3n+3, and 3n−1. If the perimeter of the triangle is 72m, what is the length of each side?
Answer: 10m, 33m, and 29m
Step-by-step explanation:
n + 3n+3 + 3n-1 = 72m
7n+2=72m
7n = 72-2
n = 70/7
n = 10
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
123456-6-&55674
Step-by-step explanation:
rdcfvvzxv.
dgjjjdeasg JJ is Redding off in grad wassup I TV kitten gag ex TV ex raisin see
recall see
HELP!!
Consider the polynomial
Answer:
1. coefficient of 3rd term = 1
2. constant term= 0
The coefficient of the third term is 1 while the constant term is 0 for the given expression.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
For example 3x +5y
As per the given polynomial,
(1/2)a⁴ + 3a³ + a
Here a is a variable.
(1)
The third term is a and its coefficient is 1 as (1)a.
(2)
All terms have variable "a" thus none of the terms is constant so the constant term is 0.
Hence "For the following statement, the constant term has a coefficient of 0 and the third term has a coefficient of 1".
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Solve 7 ( x + 1 ) + 2 = 5x + 15
Answer:
x = 3
Step-by-step explanation:
7(x + 1) + 2 = 5x + 15
~Simplify left side
7x + 7 + 2 = 5x + 15
~Combine like terms
7x + 9 = 5x + 15
~Subtract 9 to both sides
7x = 5x + 6
~Subtract 5x to both sides
2x = 6
~Divide 2 to both sides
x = 3
Best of Luck!
Select the next item in the sequence.
10.172,10.983,10.994...
A. 10.972
B. 11.000
C.11.172
D.11.983
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Answer:
B. 11.000
Step-by-step explanation:
The function looks like a reflected and translated exponential function with a horizontal asymptote near y = 11.000. The rate of change is decreasing so fast that the next value is expected to be very near 10.994. The closest one among the answer choices is 11.000.
_____
First differences are 0.811 and 0.011. The latter is about 0.0136 times the former. At that rate of change, we expect the next first difference to be about 0.000149, which would make the next number in sequence be about 10.9941—very little change from 10.994.
Clearly, first differences are not constant, so the function is not linear. Ratios of the numbers are not constant, so this is not an exponential (geometric) sequence. A reflected exponential function of the type described is a good fit.
With only 3 points given, the rule is not at all obvious. The next term could legitimately be anything you like, and a rule could be made that would fit it.
I am struggling and I would be so happy if any of you helped me. Can someone help me with the last two red boxes please? The rest of the question is for reference to help solve the problem. Thank you for your time!
Answer:
I think you can go with:
The margin of error is equal to half the width of the entire confidence interval.
so try .74 ± = [ .724 , .756] as the confidence interval
Step-by-step explanation:
The tree diagram below shows the possible combinations of juice and snack that can be offered at the school fair.
A tree diagram. Orange branches to popcorn and pretzels. Grape branches to popcorn and pretzels. Apple branches to popcorn and pretzels. Grapefruit branches to popcorn and pretzels.
How many different combinations are modeled by the diagram?
6
8
12
32
Answer:
B. 8Step-by-step explanation:
The combinations are:
Orange - 2 (with popcorn and pretzels)Grape - 2 (with popcorn and pretzels)Apple - 2 (with popcorn and pretzels)Grapefruit - 2 (with popcorn and pretzels)Total number of combinations:
4*2 = 8Correct choice is B
there are 8different combinations are modeled by the diagram.
Answer:
Solution given:
orange:2
grape:2
apple:2
grapefruit:2
no of term:4
now
total no. of combination ia 4*2=8
The surface area of a cylinder?
Answer:
18. 84 ft² or 18.85 ft² when rounded to the nearest tenth
Step-by-step explanation:
2πrh+2πr²
2× 3.14 × 1 × 2= 12.56
2 × 3.14 × 1² = 6.28
12.56 + 6.28 = 18.84
Have a great day :)
Answer:
18.85 [tex]ft^2\\[/tex]
*You should run the numbers yourself as well. Sometimes different calculators will get marginally different numbers or use a different rounding for [tex]\pi[/tex] that gives a slightly different answer*
Step-by-step explanation:
Surface area of a cylinder: [tex]2\pi rh+2\pi r^2[/tex]
Where h is the height and r is the radius. Remember that the radius is half the diameter, and the diameter is a straight line that passes through a circle.
I could be wrong, but I think you had the correct equation but used the diameter in stead of the radius to get 50.36.
Radius: 1 Height: 2
Plug numbers into equation:
[tex]A=2\pi (1)(2)+2\pi (1)^2= 18.8495. . .[/tex]
I hope that helps!
i would like some help please i am stuck
Answer: -2(d) is the answer.
Step-by-step explanation:
x1 = 3
y1 = -5
x2 = -2
y2 = 5
slope (m) = rise/run = (y2 - y1)/(x2-x1)
=(5-(-5))/(-2-3)
= 10/-5
= -2
Question 4 (2 marks)
Justin works 14 hours at a normal pay rate of $24.80 per hour and 5 hours of overtime at
time and a half. How much should he be paid?
I
809 words
LE
English (Australia)
Answer:
554.7
Step-by-step explanation:
The pay=25.8*14+(25.8)*5*1.5=554.7
SOVE, REDUCE TO LOWEST TEERMS SIMPLIFY IMPROPER FRACTIONSAS MIXED FRACTIONS
A zookeeper published the following stem-and-leaf plot showing the number of lizards at each major zoo in the country:
∣
0
1
2
3
4
5
6
∣
0
6
8
8
8
0
2
6
6
7
8
1
2
6
6
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
00
10
20
30
40
50
60
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
0
0
0
0
1
0
0
6
2
2
8
6
6
8
6
6
8
7
0
0
8
0
Key:
2
∣
0
=
20
2∣0=202, vertical bar, 0, equals, 20 lizards
How many zoos have more than 26 lizards
A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
Sham n= 20 x=0.41 s=1.37
Magnet n= 20 x =0.46 s= 0.94
Identify the test statistic. F=
Identify P-Value=
What is the conclution for the hypothesis test?
A. Fail to reject the null hypothesis. There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
B. Reject the null hypothesis. There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
C.Fail to reject the null hypothesis. There is sufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
D.Reject the null hypothesis. There is sufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
Answer:
F statistic = 2.124
Pvalue = 0.0546
A. Fail to reject the null hypothesis. There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
Step-by-step explanation:
H0 : pain reduction is the same
H1 : pain reduction is varies more with sham.
Sham n= 20 x=0.41 s=1.37
Magnet n= 20 x =0.46 s= 0.94
α - level = 0.05
Using the Ftest statistic
Ftest = larger sample variance / smaller sample variance
Ftest = s1² / s2² = 1.37² / 0.94² = 1.8769 / 0.8836 = 2.124
The degree of freedom :
Numerator = n - 1 = 20 - 1 = 19
Denominator = n - 1 = 20 - 1 = 19
Pvalue(2.124, 19, 19) = 0.0546
Since ;
Pvalue > α ; WE fail to reject the Null ; Result is not significant
a² +6²
a-b
if a = 3 and b = 4
Evaluate each expression using the variable replacements.
Answer:
-45Step-by-step explanation:
let a= 3 and b= 4a² + 6² / a - b= 3² + 6² / 3 - 4= 9 + 36 / -1= 45 / -1= -45[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
raphael made 2 pies and gave half of one pie to his grandmother. he wants to share the remaining pie with his neighbors so he cuts them into pieces that are each 3/8 of a pie. How many neighbors can have a slice of pie?
A rational expression is _______ for those values of the variable(s) that make the denominator zero.
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Answer:
undefined
Step-by-step explanation:
A rational expression is undefined when its denominator is zero.
Ilang litro ng tubig ang kailangang isalin sa timba na naglalaman ng 10 000 mililitro
Answer
nghiệmTrảingu từng bước:
Which is the solution to-x/2<-4
A x<-8
B x2-8
C x <8
D x 8
Answer:
A.x<-8
Step-by-step explanation:
=1/2x<−4
=2*(1/2x)< (2)*(-4)
= x<-8
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 83 months with a variance of 81. If the claim is true, what is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors? Round your answer to four decimal places.
Answer:
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The production manager claims they have a mean life of 83 months with a variance of 81.
This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]
Sample of 146:
This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]
What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?
This is 1 subtracted by the p-value of Z when X = 81.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]
[tex]Z = -2.42[/tex]
[tex]Z = -2.42[/tex] has a p-value of 0.0078.
1 - 0.0078 = 0.9922.
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
I will give brainly.
How do you determine if a slope is positive or negative?
You have to find the slope .
How?
Take 2points
(x1,y1)(x2,y2)Slope formula[tex]\\ \rm\Rrightarrow \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Step-by-step explanation:
What the Slope Means A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises.
Previous studies suggest that use of nicotine-replacement therapies and antidepressants can help people stop smoking. The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment.
In this experiment researchers randomly assigned smokers to treatments. Of the 162 smokers taking a placebo, 28 stopped smoking by the 8th day. Of the 272 smokers taking only the antidepressant buproprion, 82 stopped smoking by the 8th day.
Calculate the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment). (The standard error is about 0.0407. Use critical value z = 2.576.)
( ), ( )
Round your answer to three decimal places. Put lower bound in the first box and upper bound in the second box.
Using the z-distribution, it is found that the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm zs[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.s is the standard error.In this problem, we are given that z = 2.576, s = 0.0407. The sample mean is the difference of the proportions, hence:
[tex]\overline{x} = \frac{28}{162} - \frac{82}{272} = -0.129[/tex]
Then, the bounds of the interval are given by:
[tex]\overline{x} - zs = -0.129 - 2.576(0.0407) = -0.234[/tex]
[tex]\overline{x} + zs = -0.129 + 2.576(0.0407) = -0.024[/tex]
The 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).
More can be learned about the z-distribution at https://brainly.com/question/25890103
A building 51 feet tall casts a shadow 48 feet long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue? Choose an answer
Answer: 17 feet
Step-by-step explanation:
51/48 = x/16
(51)(16)/48
The statute is 17 feet tall.
What are the similar triangles?Similar triangles are the triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion.
What is the ratio of any two corresponding sides of similar triangles?The ratio of any corresponding sides in two equiangular triangles is always the same.
Let's visualize the situation according to the given question.
AB is the building ,whose height is 51f
BC is the shadow of the building AB, whose length is 48ft.
QR is the shadow of the tower statue, whose length is 16feet.
Let the height of the statue PR be h feet.
In triangle ACB and triangle PRQ
∠ACB = ∠PRQ = 90 degrees
( the objects and shadows are perpendicular to each other)
∠BAC = ∠QPR
( sunray falls on the pole and tower at the same angle, at the same time )
⇒ΔACB similar to ΔPRQ ( AA criterion)
Therefore, the ratio of any two corresponding sides in equiangular triangles is always same.
⇒ AC/CB = PR/RQ
⇒[tex]\frac{51}{48} =\frac{h}{16}[/tex]
⇒ h = [tex]\frac{(51)(16)}{48}[/tex]
⇒ h = 17 feet.
Hence, the statute is 17 feet tall.
Learn more about the similar triangle here:
brainly.com/question/25882965
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If x+y=8 and xy =15 find the value of x³+y³.
Answer:
152Step-by-step explanation:
let x= 5 and y= 3x + y = 85 + 3 = 8xy = 155 × 3 = 15x³ + y³ = ?5³ + 3³ = ?125 + 27 = 152[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
